An analysis of the diffusion-convection problem by the boundary element method

A boundary element numerical scheme for the two‐dimensional convection–diffusion equation

“…To apply the BEM it is necessary to transform the differential equation that governs the analysed problem, in this case expression (3), into a boundary integral equation (BIE in the scientific where all the terms not brought together in the second-order differential operator L have been grouped in (x, t). Applying the weighted residual technique to Equation (5) in the domain ∈ E 2 , the following domain integrals appear · L[] dV = · (x, t) dV (6) where is the fundamental solution that verifies the following differential equation:…”

“…Various numerical methods have been used to solve physical problems governed by this type of equation in the last three decades. A brief look at the scientific publications of the last 30 years shows the boundary elements method (BEM) being applied to a great variety of phenomena governed by this equation, such as those of 2064 L. M. ROMERO AND F. G. BENITEZ a magnetic field generated by a moving conductor [2], convective heat transfer [3], heat transfer in a continuous casting process [4], mass and charge transfer in electrochemical cells [5,6], volumetric transport of surfactant with semi-infinite progression of a bubble in capillary tubes [7], propagation of a contaminant in a fluid medium, etc. The approach of the BEM to the problem of traffic in cities or large towns with dense road networks was first formulated one decade ago [8].…”

Numerical solution of convection-diffusion problems at high Péclet number using boundary elements

“…[1][2][3][4][5][6][7][8][9][10][11][12] However, since the BEM formulation requires the evaluation of singular integrals, oscillations may develop at high values of Pe if this integration is not properly carried out. Very few authors have applied the BEM to problems with high Pe.…”